Vertex split connectivity prediction for improved progressive mesh compression

ABSTRACT

An encoder includes a processor and a memory. The encoder may perform a method of progressive compression. In one example implementation, the method may include identifying a pair of partitioning vertices to be connected to a split vertex associated with a collapse of an edge, creating the split vertex by collapsing the edge, encoding partitioning vertex information associated with the pair of partitioning vertices, the encoding of the partitioning vertex information based on an ordering of vertices of an umbrella of the split vertex, and the ordering of vertices of the umbrella determined based on a geometric shape and connectivity of the umbrella, and generating vertex split information that includes the partitioning vertex information. In another example implementation, the method may include entropy encoding the vertex split information prior to being transmitted.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is related to U.S. application Ser. No. 15/951,963, filed on Apr. 12, 2018, and U.S. application Ser. No. 15/951,944, filed on Apr. 12, 2018, the disclosures of both the applications are incorporated by reference herein in their entirety.

FIELD

This application relates, generally, to mesh compression, and specifically, to progressive mesh compression.

BACKGROUND

Progressive mesh compression (or progressive compression) is the encoding of mesh geometry in stages with each stage generating information related to mesh connectivity, positions, and other attributes. Each successive stage results in a coarser level of detail (LOD) of the model, and the encoding of the next LOD takes advantage of the information already contained in the previous LOD. This is relevant for transmitting high resolution models via the Internet as the user on the receiving end (e.g., a client, a client device, or an application) does not have to wait until the entire model is received from the server. The client can quickly display lower resolution LODs of the model before the information associated with higher resolution LODs is received at the client device.

SUMMARY

In one aspect, a method includes a computer-implemented method of progressive mesh compression. In one example implementation, the method may include identifying a pair of partitioning vertices to be connected to a split vertex associated with a collapse of an edge, creating the split vertex by collapsing the edge, encoding partitioning vertex information associated with the pair of partitioning vertices, the encoding of the partitioning vertex information based on an ordering of vertices of an umbrella of the split vertex, and the ordering of vertices of the umbrella determined based on a geometric shape and connectivity of the umbrella, and generating vertex split information that includes the partitioning vertex information. In another example implementation, the method may include entropy encoding the vertex split information prior to being transmitted.

BRIEF DESCRIPTION OF THE DRAWINGS

Example implementations will become more fully understood from the detailed description given herein below and the accompanying drawings, wherein like elements are represented by like reference numerals, which are given by way of illustration only and thus are not limiting of the example implementations and wherein:

FIG. 1A illustrates a portion of a geometric model (or an image of a geometric model) being compressed using an edge collapse operation, according to at least one example implementation.

FIG. 1B illustrates a portion of a geometric model (or an image of a geometric model) being compressed using another edge collapse operation, according to at least one example implementation.

FIG. 2A illustrates a full-edge collapse operation, according to at least one example implementation.

FIG. 2B illustrates a half-edge collapse operation, according to at least one example implementation.

FIG. 3A illustrates progressive compression, according to at least one example implementation.

FIG. 3B illustrates progressive compression, according to at least another example implementation.

FIG. 4 illustrates vertex split connectivity prediction, according to at least one example implementation.

FIG. 5 illustrates a flowchart of a method of vertex split connectivity prediction, according to at least one example implementation.

FIG. 6 illustrates an example of a computer device and a mobile computer device according to at least one example implementation.

It should be noted that these Figures are intended to illustrate the general characteristics of methods, structure, or materials utilized in certain example implementations and to supplement the written description provided below. These drawings are not, however, to scale and may not precisely reflect the precise structural or performance characteristics of any given implementation, and should not be interpreted as defining or limiting the range of values or properties encompassed by example implementation. The use of similar or identical reference numbers in the various drawings is intended to indicate the presence of a similar or identical element or feature.

DETAILED DESCRIPTION

In one implementation, an encoder may determine a priority value for each edge of a plurality of edges, the priority value of an edge of the plurality of edges determined based on an error metric value and an estimated encoding cost associated with the edge. The encoder may further determine a set of edges from the plurality of edges for collapse based on the priority values, collapse the set of edges and generate vertex split information, and transmit the generated vertex split information in response to a message received from a decoder. In some implementation, the encoder entropy encode the vertex split information prior to being transmitted.

FIG. 1A illustrates a portion of a geometric model 100 being compressed using an edge collapse operation, according to at least one example implementation. In FIG. 1A, area 102 of the geometric model 100 represents an area which may be compressed using an improved progressive mesh compression. In one example implementation, the area 102 may be compressed using a full-edge collapse operation (or using a full-edge collapse operator) that is described in detail below in reference to FIG. 2A. During progressive mesh compression, an encoder may generate a plurality of LODs and associated vertex split records. A LOD and associated vertex split records may be generated by collapsing an input mesh with successive batches (e.g. one or more batches) of edge collapse operators until a very coarse mesh is generated or there are no more edges for collapse (e.g., error metric value may be too high for the LOD for edge collapse).

FIG. 1B illustrates a portion of a geometric model 150 being compressed using another edge collapse operation, according to at least one example implementation. In FIG. 1B, area 152 of the geometric model 150 represents an area which may be compressed using an improved progressive mesh compression. In one example implementation, the area 152 may be compressed using a half-edge collapse operation (or using a half-edge collapse operator) that is described in detail below in reference to FIG. 2B.

FIG. 2A illustrates a full-edge collapse operation 200, according to at least one example implementation.

In FIG. 2A, an edge 206 connecting vertices 202, 210 may be collapsed via a full-edge collapse operation (e.g., using a full-edge collapse operator). In such a full-edge collapse operation, the two vertices 202, 210 are merged into one vertex (e.g., a merged vertex, a split vertex, etc.) and a new vertex 218 is generated. The location of the new vertex 218 may be determined based on, for example, minimizing an error associated with the collapse of the edge 206 (e.g., minimizing the associated local error).

The full-edge collapse operation requires higher number of bits (for instance, when compared to the half-edge collapse operation described below in reference to FIG. 2B) for encoding the two residuals between the merged vertex 218 and its two ancestors 202, 210 so that a decoder can properly reverse the full-edge collapse operation during decoding. During the full-edge collapse operation, as the edge 206 is being collapsed, the edges 204 and 208 are collapsed into a new edge (e.g., edge 216) and edges 222 and 224 are collapsed into another new edge (e.g., edge 226). Vertices 212 and 214 illustrate the merging of vertices 202 and 204 during transition of the full-edge operation. The collapsing of an edge (e.g., using a full-edge collapse operation) and the merging of the vertices, as described above, may generate a LOD (e.g., lower LOD) and associated vertex split records. The vertex split records are used by the decoder to decode (e.g., re-construct) the vertices and/or the edges that were encoded (e.g., collapsed, merged, etc.) during the full-edge collapse operation.

FIG. 2B illustrates a half-edge collapse operation 250, according to at least one example implementation.

In FIG. 2B, the edge 206 connecting vertices 202, 210 may be collapsed via a half-edge collapse operation (e.g., using a half-edge collapse operator). In such a half-edge collapse operation, one of the two vertices (e.g., vertex 210) may be merged into another vertex (e.g., vertex 202), and data is generated so that the decoder may regenerate the vertices/edges during decoding.

The half-edge collapse operation requires a lower number of bits (for instance, when compared to the full-edge collapse operation described above in reference to FIG. 2A) as only one residual associated with the vertex that is merged (e.g., vertex 210) has to be encoded to reverse the half-edge collapse operation during decoding. During the half-edge collapse operation, as the vertex 210 is being merged into vertex 202, the edge 208 is collapsed into the edge 204 and the edge 224 is collapsed into edge 222. Vertex 234 illustrates the merging of the vertex 210 into the vertex 202 during transition of the half-edge collapse operation. The collapsing/merging of edges and/or merging of vertices using half-edge collapse operations, as described above, may generate a LOD (e.g., lower LOD) and associated vertex split records. The vertex split records are used by the decoder to decode (e.g., re-construct) the vertices and/or the edges that were encoded (e.g., collapsed, merged, etc.) during the half-edge collapse operation. Although, the half-edge collapse operation may require lower number of bits (for instance, when compared to full-edge collapse operation) for representing the information that is required for decoding, the distortion rate may be higher (e.g., more distorted lower LODs).

FIG. 3A illustrates progressive compression mechanism 300, according to at least one example implementation. FIG. 3B illustrates progressive compression mechanism 350, according to at least another example implementation.

A sequence of levels of detail (LODs) may be created (or generated) during progressive compression by decimating an input mesh with successive batches of edge collapses (for example, using edge collapse operators) until a very coarse mesh is generated (or no more edges are available for collapse as error metric values may be too high for the LOD for edge collapses). A batch of edge collapses may include collapsing a subset of edges of a current mesh.

During progressive mesh compression, edges must form an independent set of edges so that they could be collapsed without interference from (or being blocked by) other edges in the immediate neighborhood (e.g., vicinity). A set of edges may be defined as an independent set of edges if the set of edges are sufficiently separated from each other such that each edge of the set of edges may be collapsed without being interfered. For example, in FIG. 3A, an edge 302, which may be a part of independent set of edges, may be collapsed without interference from other edges (e.g., edges 304) in the vicinity. However, the edges 304 which are in the vicinity of the edge 302 may be blocked from being collapsed by the edge 302. The edges 304 that are being blocked (e.g., from being collapsed) by another edge (e.g., edge 302) are generally referred to as blocked edges and cannot be collapsed in the current round (e.g., while generating the current LOD). That is, the edges 304 cannot be collapsed in the same round as the edge 302. However, one or more of the edges 304 may become part of another independent set of edges during a later round of edge collapses to generate another LOD.

Similarly, in FIG. 3B, in addition to the edge 302, edge 352, may be a part of the independent set of edges and may be collapsed without interference from other edges (e.g., 354 or 304) in the vicinity of the edge 352. However, the edges 354 which are in the vicinity of the edge 352 may be blocked from being collapsed by the edge 352. The edges 354 that are blocked (e.g., from being collapsed) by another edge (e.g., edge 352) are referred to as blocked edges and cannot be collapsed in the current round (e.g., while generating the current LOD). That is, the edges 354 cannot be collapsed in the same round as the edge 352. However, one or more of the edges 354 may become part of another independent set of edges during a later round of edge collapses to generate another LOD.

In some implementations, for example, the edges 302 and 352 may be collapsed using full-edge collapse operations (e.g., described above in detail in reference to FIG. 2A) or half-edge collapse operations (e.g., described above in detail in reference to FIG. 2B). In some other implementations, one LOD may be generated using one type of edge-collapse operations (e.g., half-edge or full-edge collapse operations) and/or the following LOD may be generated using another type of edge-collapse operations (e.g. full-edge or half-edge collapse operators) to achieve a balance between quality (e.g., distortion) and cost (e.g., bit rate or bits per vertex).

In progressive mesh compression, each edge collapse may be associated with an error (e.g., an error metric value) when the edge is collapsed. The error metric value reflects (e.g., represents) the affect of the edge collapse on the quality of the mesh. In other words, the error metric value associated with an edge collapse indicates how the quality of the mesh may be (e.g., negatively) impacted by the collapse of the edge. Therefore, to avoid collapsing edges that are too expensive (e.g., major affect on the quality of the mesh, etc.), the edges may be sorted (e.g., prioritized) based on their associated error metric values prior to being selected for collapse (or prior to being added to an independent set of edges). For example, the edges may be sorted based on their error metric values and the edge with the lowest associated error metric value queued first. In one example implementation, as the edges of the input mesh are being selected, the edges that are not being blocked are added to form (or create) an independent set of edges (e.g., first independent set of edges) and edges in the vicinity of an edge that may be blocked are not considered for collapse in the current round. The adding of edges to the independent set of edges may continue until all edges are blocked or error metric values are above a corresponding threshold.

As a batch of edges is collapsed, a lower LOD (e.g., lower resolution or coarser LOD) is generated along with additional information (e.g., vertex split information) that allows the decoder to recover the previous LOD (e.g. higher resolution LOD). In some implementation, the information generated during the generating of a LOD may include, for example, a header with initial information for the decoder (e.g., indicating whether full-edge or half-edge operations were performed); information on how the encoded vertices are to be split into edges at the decoder; information how the vertices (e.g., split vertices) are connected to their surrounding vertices (neighbors of the split vertex); information necessary for the recovery of positions of the split vertices; and/or texture coordinates or any other optional attributes.

In some implementations, for example, an independent set of edges for collapse may be determined by adding next best edges that are not blocked based on error metric values (e.g., quadric error metric values, Hausdorff distance values, etc.) associated with the edges. However, this may not be the most efficient method as the error metric values do not take into consideration the residuals (or residual values) or encoding costs associated with edge collapses. Therefore, the proposed encoding cost aware edge selection for improved progressive mesh compression describes an approach where the independent set of edges (e.g., for a LOD) may be determined based on priority values assigned to each edge of a plurality of edges of a mesh. In some implementations, the priority value of an edge may be determined based on, for example, an error metric value and an estimated encoding cost associated with the edge. For example, when two near-by edges have relatively similar (e.g., close) error metric values, the proposed encoding cost aware edge selection mechanism takes into consideration their associated encoding costs as well to select the edges. That is, a combination of the error metric value and residual value is compared to select the better edge as the selected edge may provide for better compression rates, for example, during the entropy encoding of the residual values.

The present disclosure discloses a mechanism to predict the direction of a new edge, for example, when new edges are being re-created from a split vertex during decoding. The split vertex may have been created during encoding by collapse of an edge between two vertices. In one implementation, the encoder may predict the partitioning vertices by computing the diameter of the umbrella by determining a pair of vertices that are furthest apart. This assists in the predicting the direction of the new edge. Then, two opposing vertices are determined as the most likely partitioning vertices.

In some implementations, the present disclosure may include a method for vertex split connectivity prediction. The method may include identifying a pair of partitioning vertices to be connected to a split vertex associated with a collapse of an edge, creating the split vertex by collapsing the edge, encoding partitioning vertex information associated with the pair of partitioning vertices, the encoding of the partitioning vertex information based on an ordering of vertices of the umbrella of the split vertex, and the ordering of vertices of the umbrella determined based on a geometric shape and connectivity of the umbrella, and generating vertex split information that includes the partitioning vertex information.

FIG. 4 illustrates a vertex split connectivity prediction mechanism 400 for progressive mesh compression, according to at least one example implementation.

The encoder identifies vertices 402 and 404 (as shown in 400) as the partitioning vertices as it is prior to the start of the collapse. In some implementations, the diameter 424 may be determined based on maximum distance possible between the vertices (as shown in 420) and a perpendicular bisector 452 is determined (as shown in 450). Once the perpendicular bisector 452 is determined, the pair of vertices closest to the perpendicular bisector 452 are determined and sorted as shown in 460, as described in detail below in reference to FIG. 5.

FIG. 5 illustrates a flowchart 500 of a method of progressive mesh compression. In one implementation, for example, the method may be performed by an encoder and may include vertex split connectivity prediction to improve progressive mesh compression.

At block 510, an encoder may identify a pair of partitioning vertices to be connected to a split vertex associated with a collapse of an edge. For example, in one implementation, the encoder may identify a pair of partitioning vertices (e.g., vertices 402, 404) to be connected to a split vertex associated with a collapse of an edge. The encoder can identify the pair of partitioning vertices as the identifying takes place prior to collapsing the edge.

At block 520, the encoder may create the split vertex by collapsing the edge. For example, in one implementation, the encoder may create the split vertex (e.g., split vertex 422 by collapsing edge 406. In one implementation, the edge 406 may be collapsed using a half-edge or a full-edge collapse operation. In another implementation, the edge 404 may be collapsed using mid-point collapse operation.

At block 530, the encoder may encode partitioning vertex information associated with the pair of partitioning vertices, the encoding of the partitioning vertex information based on an ordering of vertices of an umbrella of the split vertex, and the ordering of vertices of the umbrella determined based on a geometric shape and connectivity of the umbrella. For example, in one implementation, the encoder may encode partitioning vertex information associated with the pair of partitioning vertices (e.g., vertices 402, 404). The partitioning vertex information assists the decoder in identifying the partitioning vertices during decoding. The encoding of the partitioning vertex information may be based on an ordering of vertices of the umbrella (e.g., ordering of vertices, e.g., 426, 428, 432, 434, 436, 438, 440, and 442) of the split vertex (e.g., split vertex 422). The ordering of vertices of the umbrella is determined based on a geometric shape and connectivity of the umbrella, as described above in reference to FIG. 4. The ordering of vertices of the umbrella, for example, may also be defined as ordering of the vertices connected to the split vertex or associated with the split vertex.

In some implementations, the ordering of the vertices of the umbrella may be determined based on determining a diameter of the umbrella, the diameter being determined based on a maximum possible distance between a pair of the vertices of the umbrella, determining a distance between each of the vertices of the umbrella and a perpendicular bisector of the diameter, and sorting the vertices of the umbrella in an increasing order of the determined distance. For example, the diameter 424 may be determined based on a maximum possible distance between a pair of the vertices of the umbrella (e.g., distance between vertices 426 and 428). In other words, the diameter 424 may be based on determining distances between each possible pair of the vertices (e.g., vertices 426 and 442, 426 and 440, 440 and 438, 426 and 428, etc.) and considering a maximum distance that is determined between two vertices as the diameter. Once the diameter 424 is determined, a perpendicular bisector 452 may be determined and a distance between each vertex of the umbrella and the perpendicular bisector 452 of the diameter 424 are determined. The perpendicular bisector 452 is perpendicular to the diameter 424 and splits the diameter 424 into two equal parts. In other words, the distance from each vertex of the umbrella and perpendicular bisector 452 is determined.

The encoder may sort the vertices of the umbrella based on an increasing order of the determined distance. For instance, vertices of the umbrella may be sorted as shown in 460 of FIG. 4. In one example implementation, the encoder may determine that vertices 432 and 438 may have the shortest distance to the perpendicular bisector 452, as represented by 1 and 2 (e.g., 460 of FIG. 4). In other words, the vertices are sorted based on their distances (e.g., vertex with the shortest distance sorted first) from the perpendicular bisector 452 of the diameter 424. In one implementation, the two vertices that have the shortest distance from the perpendicular bisector 452 may be considered as the partitioning vertices. In some implementations, for example, the vertices the pair of vertices that are closest to the perpendicular bisector 452 and on opposite sides of the diameter 424 may be considered as the partitioning, depending on the geometry of the input (e.g., to avoid determining vertices on same sides of the diameter as the partitioning vertices, which however may depend on the geometry of the mesh).

At block 540, the encoder may generate vertex split information that includes the partitioning vertex information. For example, in one implementation, the encoder may generate vertex split information which may include the partitioning vertex information. In some implementations, the encoder for each sorted vertex may add a 0 in the stream if the vertex is partitioning vertex and a 1 otherwise. Once the encoder encounters two partitioning vertices, the encoder stops encoding any more vertices as the encoder has already encoded the two partitioning vertices which the decoder needs for decoding.

FIG. 6 shows an example of a computer device 600 and a mobile computer device 650, which may be used with the techniques described here. Computing device 600 is intended to represent various forms of digital computers, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other appropriate computers. Computing device 650 is intended to represent various forms of mobile devices, such as personal digital assistants, cellular telephones, smart phones, and other similar computing devices. The components shown here, their connections and relationships, and their functions, are meant to be exemplary only, and are not meant to limit implementations of the inventions described and/or claimed in this document.

Computing device 600 includes a processor 602, memory 604, a storage device 606, a high-speed interface 608 connecting to memory 604 and high-speed expansion ports 610, and a low speed interface 612 connecting to low speed bus 614 and storage device 606. Each of the components 602, 604, 606, 608, 610, and 612, are interconnected using various busses, and may be mounted on a common motherboard or in other manners as appropriate. The processor 602 can process instructions for execution within the computing device 600, including instructions stored in the memory 604 or on the storage device 606 to display graphical information for a GUI on an external input/output device, such as display 616 coupled to high speed interface 608. In other implementations, multiple processors and/or multiple buses may be used, as appropriate, along with multiple memories and types of memory. Also, multiple computing devices 600 may be connected, with each device providing portions of the necessary operations (e.g., as a server bank, a group of blade servers, or a multi-processor system).

The memory 604 stores information within the computing device 600. In one implementation, the memory 604 is a volatile memory unit or units. In another implementation, the memory 604 is a non-volatile memory unit or units. The memory 604 may also be another form of computer-readable medium, such as a magnetic or optical disk.

The storage device 606 is capable of providing mass storage for the computing device 600. In one implementation, the storage device 606 may be or contain a computer-readable medium, such as a floppy disk device, a hard disk device, an optical disk device, or a tape device, a flash memory or other similar solid state memory device, or an array of devices, including devices in a storage area network or other configurations. The computer program product can be tangibly embodied in an information carrier. The computer program product may also contain instructions that, when executed, perform one or more methods, such as those described above. The information carrier is a computer- or machine-readable medium, such as the memory 604, the storage device 606, or memory on processor 602.

The high speed controller 608 manages bandwidth-intensive operations for the computing device 600, while the low speed controller 612 manages lower bandwidth-intensive operations. Such allocation of functions is exemplary only. In one implementation, the high-speed controller 608 is coupled to memory 604, display 616 (e.g., through a graphics processor or accelerator), and to high-speed expansion ports 610, which may accept various expansion cards (not shown). In the implementation, low-speed controller 612 is coupled to storage device 606 and low-speed expansion port 614. The low-speed expansion port, which may include various communication ports (e.g., USB, Bluetooth, Ethernet, wireless Ethernet) may be coupled to one or more input/output devices, such as a keyboard, a pointing device, a scanner, or a networking device such as a switch or router, e.g., through a network adapter.

The computing device 600 may be implemented in a number of different forms, as shown in the figure. For example, it may be implemented as a standard server 620, or multiple times in a group of such servers. It may also be implemented as part of a rack server system 624. In addition, it may be implemented in a personal computer such as a laptop computer 622. Alternatively, components from computing device 600 may be combined with other components in a mobile device (not shown), such as device 650. Each of such devices may contain one or more of computing device 600, 650, and an entire system may be made up of multiple computing devices 600, 650 communicating with each other.

Computing device 650 includes a processor 652, memory 664, an input/output device such as a display 654, a communication interface 666, and a transceiver 668, among other components. The device 650 may also be provided with a storage device, such as a microdrive or other device, to provide additional storage. Each of the components 650, 652, 564, 654, 666, and 668, are interconnected using various buses, and several of the components may be mounted on a common motherboard or in other manners as appropriate.

The processor 652 can execute instructions within the computing device 650, including instructions stored in the memory 664. The processor may be implemented as a chipset of chips that include separate and multiple analog and digital processors. The processor may provide, for example, for coordination of the other components of the device 650, such as control of user interfaces, applications run by device 650, and wireless communication by device 650.

Processor 652 may communicate with a user through control interface 658 and display interface 656 coupled to a display 654. The display 654 may be, for example, a TFT LCD (Thin-Film-Transistor Liquid Crystal Display) or an OLED (Organic Light Emitting Diode) display, or other appropriate display technology. The display interface 656 may comprise appropriate circuitry for driving the display 654 to present graphical and other information to a user. The control interface 658 may receive commands from a user and convert them for submission to the processor 652. In addition, an external interface 662 may be provide in communication with processor 652, to enable near area communication of device 650 with other devices. External interface 662 may provide, for example, for wired communication in some implementations, or for wireless communication in other implementations, and multiple interfaces may also be used.

The memory 664 stores information within the computing device 650. The memory 664 can be implemented as one or more of a computer-readable medium or media, a volatile memory unit or units, or a non-volatile memory unit or units. Expansion memory 674 may also be provided and connected to device 650 through expansion interface 672, which may include, for example, a SIMM (Single In Line Memory Module) card interface. Such expansion memory 674 may provide extra storage space for device 650, or may also store applications or other information for device 650. Specifically, expansion memory 674 may include instructions to carry out or supplement the processes described above, and may include secure information also. Thus, for example, expansion memory 674 may be provide as a security module for device 650, and may be programmed with instructions that permit secure use of device 650. In addition, secure applications may be provided via the SIMM cards, along with additional information, such as placing identifying information on the SIMM card in a non-hackable manner.

The memory may include, for example, flash memory and/or NVRAM memory, as discussed below. In one implementation, a computer program product is tangibly embodied in an information carrier. The computer program product contains instructions that, when executed, perform one or more methods, such as those described above. The information carrier is a computer- or machine-readable medium, such as the memory 664, expansion memory 674, or memory on processor 652, that may be received, for example, over transceiver 668 or external interface 662.

Device 650 may communicate wirelessly through communication interface 666, which may include digital signal processing circuitry where necessary. Communication interface 666 may provide for communications under various modes or protocols, such as GSM voice calls, SMS, EMS, or MMS messaging, CDMA, TDMA, PDC, WCDMA, CDMA2000, or GPRS, among others. Such communication may occur, for example, through radio-frequency transceiver 668. In addition, short-range communication may occur, such as using a Bluetooth, Wi-Fi, or other such transceiver (not shown). In addition, GPS (Global Positioning System) receiver module 670 may provide additional navigation- and location-related wireless data to device 650, which may be used as appropriate by applications running on device 650.

Device 650 may also communicate audibly using audio codec 660, which may receive spoken information from a user and convert it to usable digital information. Audio codec 660 may likewise generate audible sound for a user, such as through a speaker, e.g., in a handset of device 650. Such sound may include sound from voice telephone calls, may include recorded sound (e.g., voice messages, music files, etc.) and may also include sound generated by applications operating on device 650.

The computing device 650 may be implemented in a number of different forms, as shown in the figure. For example, it may be implemented as a cellular telephone 680. It may also be implemented as part of a smart phone 682, personal digital assistant, or other similar mobile device.

Various implementations of the systems and techniques described here can be realized in digital electronic circuitry, integrated circuitry, specially designed ASICs (application specific integrated circuits), computer hardware, firmware, software, and/or combinations thereof. These various implementations can include implementation in one or more computer programs that are executable and/or interpretable on a programmable system including at least one programmable processor, which may be special or general purpose, coupled to receive data and instructions from, and to transmit data and instructions to, a storage system, at least one input device, and at least one output device. Various implementations of the systems and techniques described here can be realized as and/or generally be referred to herein as a circuit, a module, a block, or a system that can combine software and hardware aspects. For example, a module may include the functions/acts/computer program instructions executing on a processor (e.g., a processor formed on a silicon substrate, a GaAs substrate, and the like) or some other programmable data processing apparatus.

Some of the above example embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe the operations as sequential processes, many of the operations may be performed in parallel, concurrently or simultaneously. In addition, the order of operations may be re-arranged. The processes may be terminated when their operations are completed, but may also have additional steps not included in the figure. The processes may correspond to methods, functions, procedures, subroutines, subprograms, etc.

Methods discussed above, some of which are illustrated by the flow charts, may be implemented by hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented in software, firmware, middleware or microcode, the program code or code segments to perform the necessary tasks may be stored in a machine or computer readable medium such as a storage medium. A processor(s) may perform the necessary tasks.

Specific structural and functional details disclosed herein are merely representative for purposes of describing example embodiments. Example embodiments, however, be embodied in many alternate forms and should not be construed as limited to only the embodiments set forth herein.

It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of example embodiments. As used herein, the term and/or includes any and all combinations of one or more of the associated listed items.

It will be understood that when an element is referred to as being connected or coupled to another element, it can be directly connected or coupled to the other element or intervening elements may be present. In contrast, when an element is referred to as being directly connected or directly coupled to another element, there are no intervening elements present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., between versus directly between, adjacent versus directly adjacent, etc.).

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments. As used herein, the singular forms a, an, and the are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms comprises, comprising, includes and/or including, when used herein, specify the presence of stated features, integers, steps, operations, elements and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and/or groups thereof

It should also be noted that in some alternative implementations, the functions/acts noted may occur out of the order noted in the figures. For example, two figures shown in succession may in fact be executed concurrently or may sometimes be executed in the reverse order, depending upon the functionality/acts involved.

Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which example embodiments belong. It will be further understood that terms, e.g., those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

Portions of the above example implementations and corresponding detailed description are presented in terms of software, or algorithms and symbolic representations of operation on data bits within a computer memory. These descriptions and representations are the ones by which those of ordinary skill in the art effectively convey the substance of their work to others of ordinary skill in the art. An algorithm, as the term is used here, and as it is used generally, is conceived to be a self-consistent sequence of steps leading to a desired result. The steps are those requiring physical manipulations of physical quantities. Usually, though not necessarily, these quantities take the form of optical, electrical, or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. It has proven convenient at times, principally for reasons of common usage, to refer to these signals as bits, values, elements, symbols, characters, terms, numbers, or the like.

In the above illustrative implementations, reference to acts and symbolic representations of operations (e.g., in the form of flowcharts) that may be implemented as program modules or functional processes include routines, programs, objects, components, data structures, etc., that perform particular tasks or implement particular abstract data types and may be described and/or implemented using existing hardware at existing structural elements. Such existing hardware may include one or more Central Processing Units (CPUs), digital signal processors (DSPs), application-specific-integrated-circuits, field programmable gate arrays (FPGAs) computers or the like.

It should be borne in mind, however, that all of these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities. Unless specifically stated otherwise, or as is apparent from the discussion, terms such as processing or computing or calculating or determining of displaying or the like, refer to the action and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical, electronic quantities within the computer system's registers and memories into other data similarly represented as physical quantities within the computer system memories or registers or other such information storage, transmission or display devices.

Note also that the software implemented aspects of the example implementations are typically encoded on some form of non-transitory program storage medium or implemented over some type of transmission medium. The program storage medium may be magnetic (e.g., a floppy disk or a hard drive) or optical (e.g., a compact disk read only memory, or CD ROM), and may be read only or random access. Similarly, the transmission medium may be twisted wire pairs, coaxial cable, optical fiber, or some other suitable transmission medium known to the art. The example implementations not limited by these aspects of any given implementation.

Lastly, it should also be noted that whilst the accompanying claims set out particular combinations of features described herein, the scope of the present disclosure is not limited to the particular combinations hereafter claimed, but instead extends to encompass any combination of features or implementations herein disclosed irrespective of whether or not that particular combination has been specifically enumerated in the accompanying claims at this time.

While example implementations may include various modifications and alternative forms, implementations thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that there is no intent to limit example implementations to the particular forms disclosed, but on the contrary, example implementations are to cover all modifications, equivalents, and alternatives falling within the scope of the claims. Like numbers refer to like elements throughout the description of the figures. 

What is claimed is:
 1. A computer-implemented method of progressive mesh compression, comprising: identifying, by an encoder, a pair of partitioning vertices to be connected to a split vertex associated with a collapse of an edge; creating, by the encoder, the split vertex by collapsing the edge; encoding, by the encoder, partitioning vertex information associated with the pair of partitioning vertices, the encoding of the partitioning vertex information based on an ordering of vertices of an umbrella of the split vertex, and the ordering of vertices of the umbrella determined based on a distance between the vertices of the umbrella and a perpendicular bisector of a diameter of the umbrella; and generating, by the encoder, vertex split information that includes the partitioning vertex information.
 2. The method of claim 1, further comprising: entropy encoding of the vertex split information.
 3. The method of claim 1, further comprising: transmitting, from the encoder, the vertex split information to a decoder in response to a message received from the decoder.
 4. The method of claim 1, wherein the ordering of vertices of the umbrella further comprises: determining the diameter of the umbrella, the diameter being determined based on a maximum possible distance between a pair of the vertices of the umbrella; determining the distance between each of the vertices of the umbrella and the perpendicular bisector of the diameter; and sorting the vertices of the umbrella in an increasing order of the determined distance.
 5. The method of claim 4, wherein the perpendicular bisector is perpendicular to the diameter and splits the diameter into two equal halves, and wherein the pair of partitioning vertices are on opposite sides of the diameter of the umbrella.
 6. The method of claim 1, further comprising: encoding each partitioning vertex of the pair of partitioning vertices with a first value; encoding each non-partitioning vertex of the vertices of the umbrella with a second value, and wherein the first value is different from the second value; and terminating the encoding in response to encoding the two partitioning vertices.
 7. The method of claim 1, wherein the split vertex is created by collapsing the edge based on a full-edge or a half-edge collapse operation.
 8. An encoder, comprising: a processor; and a memory, the memory including instructions configured to cause the processor to: identify a pair of partitioning vertices to be connected to a split vertex associated with a collapse of an edge; create the split vertex by collapsing the edge; encode partitioning vertex information associated with the pair of partitioning vertices, the encoding of the partitioning vertex information based on an ordering of vertices of an umbrella of the split vertex, and the ordering of vertices of the umbrella determined based on a distance between the vertices of the umbrella and a perpendicular bisector of a diameter of the umbrella; and generate vertex split information that includes the partitioning vertex information.
 9. The encoder of claim 8, further comprising instructions to cause the processor to: entropy encode of the vertex split information.
 10. The encoder of claim 8, further comprising instructions to cause the processor to: transmit the vertex split information to a decoder in response to a message received from the decoder.
 11. The encoder of claim 8, further comprising instructions to cause the processor to: determine the diameter of the umbrella, the diameter being determined based on a maximum possible distance between a pair of the vertices of the umbrella; determine the distance between each of the vertices of the umbrella and the perpendicular bisector of the diameter; and sort the vertices of the umbrella in an increasing order of the determined distance.
 12. A non-transitory computer-readable storage medium having stored thereon computer executable program code which, when executed on a computer system, causes the computer system to perform a method of progressive mesh compression, comprising: identifying, by an encoder, a pair of partitioning vertices to be connected to a split vertex associated with a collapse of an edge; creating, by the encoder, the split vertex by collapsing the edge; encoding, by the encoder, partitioning vertex information associated with the pair of partitioning vertices, the encoding of the partitioning vertex information based on an ordering of vertices of an umbrella of the split vertex, and the ordering of vertices of the umbrella determined based on a distance between the vertices of the umbrella and a perpendicular bisector of a diameter of the umbrella; and generating, by the encoder, vertex split information that includes the partitioning vertex information.
 13. The computer-readable storage medium of claim 12, further comprising code for: entropy encoding of the vertex split information.
 14. The computer-readable storage medium of claim 12, further comprising code for: transmitting, from the encoder, the vertex split information to a decoder in response to a message received from the decoder.
 15. The computer-readable storage medium of claim 12, wherein the ordering of vertices of the umbrella further comprises code for: determining the diameter of the umbrella, the diameter being determined based on a maximum possible distance between a pair of the vertices of the umbrella; determining the distance between each of the vertices of the umbrella and the perpendicular bisector of the diameter; and sorting the vertices of the umbrella in an increasing order of the determined distance.
 16. The computer-readable storage medium of claim 15, wherein the perpendicular bisector is perpendicular to the diameter and splits the diameter into two equal halves, and wherein the pair of partitioning vertices are on opposite sides of the diameter of the umbrella.
 17. The computer-readable storage medium of claim 12, further comprising code for: encoding each partitioning vertex of the pair of partitioning vertices with a first value; encoding each non-partitioning vertex of the vertices of the umbrella with a second value, and wherein the first value is different from the second value; and terminating the encoding in response to encoding the two partitioning vertices.
 18. The computer-readable storage medium of claim 12, wherein the split vertex is created by collapsing the edge based on a full-edge or a half-edge collapse operation. 